Effect of strain gradient on micro-buckling behaviors in biological staggered composites

Abstract

Biological staggered composites have exceptional mechanical properties and efficient biological functions because of their hierarchical structural characteristics. The staggered structure is among the most common microstructural arrangements in biological composites, where mineral platelets have a high aspect ratio, thus inducing buckling-dominated failure under compression. However, as the scale decreases, the mechanical behavior of staggered structures exhibits significant size effects, yet their trans-scale buckling mechanisms remain unclear. Therefore, in this paper, strain gradient theory is applied to establish a trans-scale buckling model for staggered structures. Analytical solutions for buckling displacement and stress fields with size-dependent characteristics are obtained, and the regulatory mechanisms of microstructural features on macroscopic buckling behavior are identified. The results show that strain gradient effects significantly affect the material’s size-dependent behavior. The higher-order stresses in the organic layers dominate the nonlinear variation of critical buckling strength and significantly influence structural stability. Moreover, the buckling resistance performance is synergistically governed by material stiffness, geometric parameters (e.g., aspect ratio, mineral volume fraction), and characteristic length parameters. By tailoring the matching relationship between organic layer thickness and characteristic length parameters, we can optimize the strain gradient effects and interfacial stress distribution, thus providing guidance for the buckling-resistant design of staggered composites. This study deepens the understanding of biological staggered composites’ trans-scale mechanical behavior and provides a theoretical basis for the anti-buckling design of staggered structural composites.